Question

Find the value of the expression: 1 + ix^{-2} + ix^{-4} + ix^{-6} + ix^{-8} ...... upto 1001 terms

Answer 1

Step-by-step explanation:

we know= it is is gp series

here a=1

r=x^{-2}

n=1001

sum of gp series

=[a(r^n-1)]/(r-1)

=[1(x^{-2}×n-1)]/(x^{-2}-1)

=[(x^{-2n}-1)/x^{-2}-1]

=[(x^{-2×1001}-1)/(x^{-2}-1)

=[x^(-2002)-1]/[x^(-2)-1]

=x^2000 approx.